Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

ABSTRACT Introduction: The intra-oral skeletally anchored maxillary protraction (I-SAMP) has been found to be an effective treatment for skeletal Class III malocclusion. Objective: This in-silico study explored the influence of different force directions of intra-oral skeletally anchored Class III elastics on the changes in craniomaxillofacial complex, using finite element analysis. Methods: A 3-dimensional (3D) finite element model of the craniomaxillofacial bones including circummaxillary sutures was constructed with high biological resemblance. A 3D assembly of four miniplates was designed and fixed on the maxilla and mandible of the finite element model. The model was applied with 250g/force at the miniplates at three angulations (10°, 20°, and 30°) from the occlusal plane, to measure stress and displacement by using the ANSYS software. Results: The zygomaticotemporal, zygomaticomaxillary, and sphenozygomatic sutures played significant roles in the forward displacement and counterclockwise rotation of maxilla and zygoma, irrespective of the angulation of load application. The displacements and rotations of the zygomatico-maxillary complex decreased gradually with an increase in the angle of load application between miniplates from 10° to 30°. The mandible showed negligible displacement, with clockwise rotation. Conclusions: The treatment effects of I-SAMP were corroborated, with insight of displacement patterns and sutures involved, which were lacking in the previously conducted 2D and 3D imaging studies. The prescribed angulation of skeletally anchored Class III elastics should be as low as possible, since the displacement of zygomatico-maxillary complex increases with the decrease in angulation of the elastics.


INTRODUCTION
The use of skeletally anchored maxillary protraction (SAMP) for orthopedic treatment of maxillary retrognathia has reduced the dentoalveolar and skeletal side effects of toothborne devices and enhanced maxillary protraction. [1][2][3][4][5][6] The use of dentally anchored maxillary protraction (DAMP) with rapid maxillary expansion (RME) and facemask is currently limited to the deciduous or early mixed dentitions. 3 However, Intraoral Skeletally Anchored Maxillary Protraction (I-SAMP) with Class III elastics can be successfully used in the late mixed or permanent dentition phases. 4,5 By using intermaxillary elastics between miniplates on zygomatic crests of the maxilla and in the anterior mandibular region, De Clerck et al 4 introduced a new perspective to the orthopedic treatment of Class III malocclusions. With this method, intermaxillary traction can be applied almost 24 hours a day. 5 Cevidanes et al 6 found that I-SAMP had two to three millimeters more maxillary advancement than RME combined with facemask.
Originally developed by Courant, finite element method (FEM) is a computer-aided numerical technique that has been used to study the nature of stress and strain induced by orthodontic forces during tooth movement. 7 Based on the Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis 5 division of a complex structure into smaller sections called elements, FEM provides detailed information on the physiological reactions in tissues after applying orthopedic forces. 8 A FEM study in which protraction forces were applied only on maxilla at different location and directions concluded that by varying the mechanics directions, different magnitudes of forward, downward, and rotational movements of the maxilla can be achieved. 9 Although I-SAMP is an established technique for correction of skeletal Class III, currently there is a paucity of data on the optimum load and appropriate direction of Class III elastics for this type of orthopedic traction. Further, there is a need for a collective finite element study to evaluate the stress pattern and displacement in different craniofacial sutures and diverse bones of craniomaxillofacial complex, and to improve the mechanics and results of this treatment modality. Thus, the aim of this study was to explore the influence of different force directions of I-SAMP on craniomaxillofacial complex, by using the finite element analysis.
Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis 6

A) CONE BEAM COMPUTED TOMOGRAPHY RAW DATA
Cone beam computed tomography (CBCT) scan (i-CAT Vision; Hatfield, PA), (120kVp, 5mA, 130.0 FOV, 4sec) of craniomaxillofacial complex of a 10 year old female with Class III malocclusion who had a retrusive maxilla with protrusive mandible and an anterior crossbite was taken from patient's diagnostic data records. Experimental protocols were reviewed and approved by Institutional Ethical Committee (MAIDS/EC/2016/10/04).

Pre-processing
Raw volumetric reconstructive data from the CBCT scan ( Fig 1A) was saved as digital imaging and communications in medicine (DICOM) files, and then imported into finite element modeling software (Mimics 8.11, Materialise: Leuven, Belgium), and a 3D model of the patient's skull was reconstructed ( Fig 1B). The 3D model of the skull was then segmented into separate 3D models of sutures, craniofacial bones, and teeth, to refine these structures (Fig 2).
Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

Post-processing
Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis   Table 1. 10 Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis 10 Solution Nodes along the foramen magnum of occipital bone and all nodes of the cranium lying on a symmetrical plane bypassing frontal, parietal and occipital bones were fully constrained by all degrees of freedom, zero displacement and zero rotation (Fig 3). 10 Protraction forces (250g/f side) were applied in between different hooks of both maxillary and mandibular miniplates bilaterally (Fig 4). 4,5 Three analytic models ( Fig 5) were developed based on locations and angulations of the force application as in 10° angu-  Table 1: Young's modulus and Poisson's ratio for the materials used in this study.
Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

STRESS DISTRIBUTION AMONG THE MAXILLOFACIAL BONES
The magnitude of maximum von Mises stresses at three different angulations varied from 1.5 to 23.7 megaPascals, which in most of the bones decreases when the angulation of force is increasing, as depicted in Figure 6. Among all the maxillofacial Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis bones, maxilla and zygomatic bone showed highest stresses.
In the maxilla, maximum stresses were seen around the site of fixation of miniplates; while second highest von Mises stresses was perceived in zygomatic bone in the lower region of temporal process. In mandible, higher stresses were seen only at the site of miniplates fixation, ranging from 1.6 to 6.6 MPa.     Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

DISPLACEMENT PATTERN OF THE MAXILLOFACIAL BONES
The amount of displacement at each surface landmark was compared separately on the Y and Z-axes, as tabulated in Table 5.

SUPERIMPOSITIONS
In the superimposition results, the 'before' image is shown in blue mesh, while the 'after' image is displayed in a range of colors that directly resemble the amount of Y-displacement (pure protraction) or Z-displacement (vertical) following force application (Figs 10 and 11).   Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

DISCUSSION
For correction of Class III malocclusion, studies have described an array of orthodontic and orthopedic treatments, such as: Class III functional appliances, 11 chin guards, 12 splints with Class III elastics, 13 and cervical extraoral mandibular anchoring. 14  The study of differential strain patterns by Oberheim and Mao 19 showed contrasting bone-strain patterns in response to simulated orthopedic forces across zygomaticotemporal suture.
Similarly, the present study also obtained differential strain patterns along the various sutures -i.e. the zygomaticomaxillary, zygomaticotemporal, and zygomaticofrontal sutures -, as they were associated with both tensile and compressive stresses. A study by Nguyen et al 20 had found that the maxilla, the zygomas, and the maxillary incisors moved forward by one unit after the application of bone-anchored maxillary protraction. It is due to the high potential of adaptation in the zygomaticotemporal, and zygomaticofrontal sutures that displacement in both maxilla and zygomas is same (3.7mm). 21 This study also showed displacement of zygomatic arch along with maxilla as one unit, in superimpositions (Fig 9). These These results were similar to clinical findings, suggesting the reasonability and feasibility of the modeling. 8,9 If we look at the displacement values of surface landmarks of mandible, the mandible underwent negligible displacement in the form of clockwise rotation. Centre of rotation of mandible seemed to be at Gonion, as all values in all the three axes were almost zero. Previous systematic review also showed that both skeletally and dentoalveolar anchored dentofacial orthopedics resulted in the clockwise rotation of mandible and increase in lower-anterior facial height. 22 This study has provided additional information on the effect of varying angulation of Class III elastics in case of I-SAMP, which to the best of our knowledge has not been discussed in any previous studies. The corrective effect on Class III pattern by forward displacement of zygomatico-maxillary complex, as well as rotations of the maxilla and mandible, decreased gradually with an increase of the angle of load application between miniplates from 10° to 30°. Another study 23 concluded that determination Garg D, Rai P, Tripathi T, Kanase A -Effects of different force directions of intra-oral skeletally anchored maxillary protraction on craniomaxillofacial complex, in Class III malocclusion: a 3D finite element analysis

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of the traction force direction should be according to the anchorage location and skeletal characteristics of patients. The finding that the stress values of the pterygomaxillary, frontonasal, frontomaxillary, nasomaxillary and internasal sutures were higher in the 10° angulation than in the 30° (Fig 6) suggests that reducing the angulation, i.e. 10°, could transfer orthopedic forces more efficiently to these sutures.
In this study, only the initial effects of single loading were analyzed over the craniomaxillofacial complex, but not the nonlinear variations of displacement and stress occurring in long-term loading over time -a common limitation of the FEM. It should be noted that any variation in values between this study and previous studies can be attributed to the fact that we only considered forces from the intraoral Class III elastics, and not from the soft tissues such as muscles, ligaments and skin. Moreover, this finite element modeling study was performed in Freeway space state, and the upper and lower dentitions were not in contact. Hence, opposing forces from maxillary molar to mandibular molar were not deliberated.

CLINICAL RELEVANCE
This first in-silico research on the I-SAMP suggests that clinicians should be aware of the fact that the prescribed angulation of Class III elastics should be as low as possible, since the displacement of zygomatico-maxillary complex and mandible increases with the decrease in the angulation of elastics.